demand the policy makers keep on average the interest rate low. As the private sector cor-
rectly anticipates such an incentive, the precautionary stance of the monetary policy generates
a systematic boost in inflation expectations even though, unlike in Barro and Gordon (1983),
the central bank targets output at potential.9
4.1 A model-based measure of the inflation mean
This section proposes a simple strategy to measure the asymmetric preferences induced infla-
tion bias, which is defined as the difference between the model-based inflation mean and the
inflation target. The resulting expression is isomorphic to the one that Surico (2003) derives
as the difference between the optimal policies under discretion and under commitment using
an asymmetric central bank objective and a Lucas aggregate supply.
On the basis of the empirical results presented in the previous section, we impose the
restriction α =0into the first order condition of the central bank optimization problem (5).
The corresponding augmented targeting rule writes
Et-1{[- (it - i*) + (1 - ρ) (c1 (πt - π*) + c2yt + c4y2) + P(it-1 - i*)]zt-1} = 0 (9)
where the parameters are written in reduced-form for expositional convenience and zt-1 cor-
responds to the instrument set.
The maintained assumption that the target i* equals the sample mean of the interest rate,
combined with the empirically grounded restriction of a symmetric preference over inflation
allow us to uniquely identify the inflation target. To see this, notice that the constant in the
above expression becomes nothing but the convolution (—cι∏*).10 The inflation mean and its
components can then be computed by taking the unconditional expectation of equation (9),
and reads:
* c4 2 * γλ 2
E (πt) = π - ciσy = π - 2kσy (10)
9 In the theory of consumption, a precautionary motive emerges from the interaction between non-quadratic
preferences and labor income risks such as to generate above-average saving rates in periods of high uncertainty.
As shown by Kimball (1990), a sufficient condition for a precautionary saving is that the expected marginal
utility be convex in consumption. Analogously here, the above-average inflation comes from the interaction
between an asymmetric central bank objective and uncertainty about the state of the economy. Moreover, as
the expected marginal loss is concave in the output gap, this motive can be thought as a precautionary demand
for expansions.
10It is worth noticing that the assumption on the interest rate target should bias, if any, the inflation target
towards the sample mean of inflation. This suggests that our estimates are likely to understate the contribution
of the asymmetric preferences induced bias to the actual mean of US inflation.
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